Please provide a detailed solution

A massive cylinder of radius R and mass M rests on an inclined plane of angle ? with the horizontal. On the surface of the cylinder a groove of depth b is carved. A rope is wound in this slot, the free end of which is pulled with a force F (see below's pic). The coefficients of friction between the plane and the cylinder are ?stat and ?din

c) Evaluate the limit angle ?_l as a function of the depth of the groove b.

d) If the angle ? is less than the limit angle ?, evaluate the acceleration of the cylinder as a function of the force F.